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OT is a broad category that includes both commutative and non-commutative operations (in the OT literature, this is usually called the TP2 property). Most practical implementations are non-commutative, because people have only figured out how to do commutativity fairly recently. OT with commutative operations overlaps a lot with operation-based CRDT.

http://haslab.uminho.pt/ashoker/files/opbaseddais14.pdf is a good paper on this, and their idea of partially ordered logs provides theoretical support for my earlier essay about unifying operational transformation and CRDT - I'll definitely cite it in any future publications.

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So the main diff would be that CRDTs must be commutative and OTs don't have to be? Are there any other differences?

What about state-based CRDTs, how do they fit the big picture?

That's the main substantive difference. I think there are differences in flavor considering that these came from rather different literatures. I have a feeling they'll converge.

State-based CRDT involves sending the entire document model, rather than just deltas from the last state. That's fine if documents are small or deltas are big chunks, but these tend not to be good assumptions in text editing. On the flip side, they're easier to reason about because connections don't have to be stateful.

There was a paper recently about delta state CRDTs with the relevant code. C++ code for reference https://github.com/CBaquero/delta-enabled-crdts